Dot product calculator : How to use it?
The dot product calculator allows the calculation of the dot product of two vectors online from their coordinates.
Syntax :
dot_product(vector;vector)
Examples :
Analytical definition of the scalar product
It is possible to calculate the dot product of two vectors from their coordinates.
In the plan, in an orthonormal system `(O,vec(i),vec(j))` ,
`vec(u)` is a vector of coordinates (x,y) and `vec(v)` is a vector of coordinates (x',y'),
the dot product is given by the formula
xx'+yy'.
This definition can be extended to space. In a direct orthonormal system `(O,vec(i),vec(j),vec(k))`,
`vec(u)` is a vector of coordinates (x,y,z) and `vec(v)` is a vector of coordinates (x',y',z'),
the dot product is given by the formula
xx'+yy'+zz'.
Property
If `vec(u)` and `vec(v)` are orthogonal, then the dot product is zero.
Online calculation of the scalar product.
The dot product calculator allows to calculate the dot product of two vectors from their coordinates. The calculation of the scalar product online can be done with numbers or literal expressions.
Dot product calculation from numeric coordinates.
To calculate the dot product of the following vectors `vec(v)` [1;5] and `vec(u)` [1;3], enter dot_product(`[1;5];[1;3]`). After calculation the result 16 is returned.
Dot product calculation from literal coordinates.
To calculate the dot product of the following vectors `vec(v)` `[a;b-1]` and `vec(u)` `[2a;a/2]`, enter dot_product(`[a;b-1];[2a;a/2]`). After calculation the result `-a/2+(b*a)/2+2*a^2` is returned.
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